Asymptotic Study of the 2D-DQGE Solutions
We study the regularity of the solutions of the surface quasi-geostrophic equation with subcritical exponent 1/2<α≤1. We prove that if the initial data is small enough in the critical space H˙2-2α(R2), then the regularity of the solution is of exponential growth type with respect to time and its...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2014/538374 |
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| author | Jamel Benameur Mongi Blel |
| author_facet | Jamel Benameur Mongi Blel |
| author_sort | Jamel Benameur |
| collection | DOAJ |
| description | We study the regularity of the solutions of the surface quasi-geostrophic equation with subcritical exponent 1/2<α≤1. We prove that if the initial data is small enough in the critical space H˙2-2α(R2), then the regularity of the solution is of exponential growth type with respect to time and its H˙2-2α(R2) norm decays exponentially fast. It becomes then infinitely differentiable with respect to time and has value in all homogeneous Sobolev spaces H˙s(R2) for s≥2-2α. Moreover, we give some general properties of the global solutions. |
| format | Article |
| id | doaj-art-94b15e8af850496089d18301f030ffc8 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-94b15e8af850496089d18301f030ffc82025-02-03T01:08:50ZengWileyJournal of Function Spaces2314-88962314-88882014-01-01201410.1155/2014/538374538374Asymptotic Study of the 2D-DQGE SolutionsJamel Benameur0Mongi Blel1Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi ArabiaWe study the regularity of the solutions of the surface quasi-geostrophic equation with subcritical exponent 1/2<α≤1. We prove that if the initial data is small enough in the critical space H˙2-2α(R2), then the regularity of the solution is of exponential growth type with respect to time and its H˙2-2α(R2) norm decays exponentially fast. It becomes then infinitely differentiable with respect to time and has value in all homogeneous Sobolev spaces H˙s(R2) for s≥2-2α. Moreover, we give some general properties of the global solutions.http://dx.doi.org/10.1155/2014/538374 |
| spellingShingle | Jamel Benameur Mongi Blel Asymptotic Study of the 2D-DQGE Solutions Journal of Function Spaces |
| title | Asymptotic Study of the 2D-DQGE Solutions |
| title_full | Asymptotic Study of the 2D-DQGE Solutions |
| title_fullStr | Asymptotic Study of the 2D-DQGE Solutions |
| title_full_unstemmed | Asymptotic Study of the 2D-DQGE Solutions |
| title_short | Asymptotic Study of the 2D-DQGE Solutions |
| title_sort | asymptotic study of the 2d dqge solutions |
| url | http://dx.doi.org/10.1155/2014/538374 |
| work_keys_str_mv | AT jamelbenameur asymptoticstudyofthe2ddqgesolutions AT mongiblel asymptoticstudyofthe2ddqgesolutions |